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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 195

The function f f\,f is defined by f(x)=arctan⁡xf(x) = \arctan xf(x)=arctanx for x∈Rx \in \mathbb{R}x∈R.

a.

Sketch the graph of y=f(x)y = f(x)y=f(x), stating the equations of its asymptotes.

[3]
b.

Using set notation, state the range of fff.

The function g g\,g is defined by g(x)=arccos⁡xg(x) = \arccos xg(x)=arccosx, where g g\,g has its greatest possible domain.

[1]
c(i).

Using set notation, state the domain and the range of ggg.

[2]
c(ii).

Show that arccos⁡x+arcsin⁡x=π2\displaystyle \arccos x + \arcsin x = \frac{\pi}{2}arccosx+arcsinx=2π​ for −1≤x≤1-1 \leq x \leq 1−1≤x≤1.

[2]
Markscheme

3 Unit A2 1: Pure Mathematics (A-level only) Questions

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